Leo is the equivalent of Interceptor in Final Fantasy 6.
Just in case the reference is lost on some, Interceptor was PC Shadow's dog, who would randomly jump in a fight and maul one enemy for you.
Leo's presence in the material world is derived from Lucy's magic. Otherwise he'd be slowly dying as he was when he lived without a summoner. Sure at one time he acted independently, but now he's basically one of her Pokemon. Only unlike the others he can leave his Pokeball at will which is damn handy since Lucy keeps losing her gorram keys.